How domain growth is implemented determines the long term behaviour of a cell population through its effect on spatial correlations

Robert J. H. Ross; R. E. Baker; C. A. Yates

The copyright holder for this preprint (which was not peer-reviewed) is the . https://doi.org/10.1101/041509 doi: bioRxiv preprint new neighbouring agents, with agents and their neighbours moving synchronously in a growth event (except at the position of growth where two columns/rows will be separated). Therefore, the spatial correlations associated with agent proliferation (in conjunction with the dilution of agent density due to domain growth) lower the steady-state density of the agents more than the displacement of agents by domain growth counteracts the spatial correlations established by agent proliferation. In Fig. 5 the effect of GM1 on spatial correlations in both the correlation ODE model and the IBM can be seen. Importantly, we see that as the growth rate is increased the spatial correlations augment. From Fig. 4 this result is to be expected, as domain growth lowers the agent steady-state density but is not effective at reducing spatial correlations. A similar result has previously been observed in the case of agent death [25] . In addition, at the agent steady-state density the spatial correlations do not return to F = 1. This explains why the MFA incorrectly predicts the agent steady-state density, and shows why the correlation ODE model is able to correctly approximate the steady-state density of the IBM. This is because the MFA is only correct when F = 1, which is not the case in the IBM in this scenario with GM1.